deletions | additions       diff --git a/Recently_from_a_phenomenological_point__.tex b/Recently_from_a_phenomenological_point__.tex  index 3fe367e..eff11d6 100644  --- a/Recently_from_a_phenomenological_point__.tex  +++ b/Recently_from_a_phenomenological_point__.tex 
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%This study supports this even down to $v = 0.02 ~\mathrm{a.u.}$ (see Figure \ref{fig:log_stopping_power}).   %The experimental results of Nomura and Kiyota \cite{Nomura_1975} on $\mathrm{H^+ + Cu}$ film show the dependence of $S_\text{e}$ on incident velocity agrees with the calculation of Lindhard \emph{et al.} \cite{Lindhard_Scharff_Schiott}.   In this Letter we will address the problem of theoretical calculation of $S_\text{e}$ of protons in crystalline $\mathrm{Cu}$ for a wide range of available experimental velocities ($0.01~\mathrm{a.u.} ($0.02~\mathrm{a.u.}  \leq v \leq 10~\mathrm{a.u.}$). We perform our calculations by directly simulating the process of a proton traversing a crystal of $\mathrm{Cu}$ atoms, producing individual and collective electronic excitations within the TDDFT framework \cite{Correa_2012,Schleife_2012,Schleife_2014} including Ehrenfest molecular dynamics (EMD) \cite{Gross_1996,Calvayrac_2000,Mason_2007,Alonso_2008,Andrade_2009}. This method is used to calculate most microscopic quantities along the process (forces, electronic density, charges, etc); in particular, we report here calculation of $S_\text{e}$. A quantitative explanation and interpretation of our results are furnished along with a detailed experimental comparison.  %We provide a quantitative explanation and interpretation of the result and a comparison with experiments.